Cracking Electron Correlation

Abstract

After reviewing current perceptions about the electron correlation problem, a general selected configuration interaction (CI) method to calculate highly accurate energies for atoms and medium-sized molecules is described. For a given orbital basis, selected CI may be implemented to yield the best energy and corresponding wave function for given selection thresholds together with an estimate of the full CI energy. The linked cluster expansion is used as an intermediate device to reveal relationships between variational coefficients in the CI expansion. These relationships allow to predict CI coefficients that are used in an a priori and fast-to-evaluate variational estimate of individual configuration energy contributions via Brown's formula both for selection purposes, and to estimate the truncation energy error caused by unselected configurations. Concepts based on natural orbitals are used likewise for configurations not amenable to the above analysis. An application to the ground state of the Ne atom achieves an accuracy of two µhartrees using very large orbital bases, increasing accuracy more than a hundredfold and at fair computational cost.